| Summary: | This thesis mainly explores model theoretic and algebraic properties of positive characteristic Hahn fields. We show that any positive characteristic tame Hahn field F((t^Γ )) containing t is decidable in Lt, the language of valued fields with a constant symbol for t, if F and Γ are decidable. In particular, we obtain decidability of Fp((t^{1/p^∞})) and Fp((t^Q)) in Lt. This uses a new AKE-principle for equal characteristic tame fields in Lt, building on work by Kuhlmann, together with Kedlaya’s work on finite automata and algebraic extensions of function fields. In the process, we obtain an AKE-principle for tame fields in mixed characteristic and extend a theorem by Rayner on the relative algebraic closure of function fields inside Hahn fields. Furthermore, for any Hahn field containing Fp((t)), we use an approximation method described originally by Lampert to obtain a bound on the order type of elements that are algebraic over Fp((t)).
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